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C₂₉×#3156 #16816870

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

532 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 65 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(31,33)(34,35,39,43)(36,44,48,58)(37,41,49,55)(38,51,45,42)(40,52,54,47)(46,57,60,65)(50,62,59,56)(53,63,64,61);(34,36,45,52,39,48,38,47)(35,40,51,58,43,54,42,44)(37,46,59,63,49,60,50,61)(41,53,62,65,55,64,56,57);(30,31,32,33)(34,37)(35,41)(36,46)(38,50)(39,49)(40,53)(42,56)(43,55)(44,57)(45,59)(47,61)(48,60)(51,62)(52,63)(54,64)(58,65);(37,49)(41,55)(46,60)(50,59)(53,64)(56,62)(57,65)(61,63)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1888);